1. Field of the Invention
This invention relates to micromechanical resonator devices having desired mode shapes.
2. Background Art
The following references are referenced herein:    1. J. Wang, Z. Ren, and C. T.-C. Nguyen, “Self-Aligned 1.14 GHz vibrating radial-mode disk resonators,” TRANSDUCERS '03, pp. 947–950.    2. J. R. Clark, W.-T. Hsu, and C. T.-C. Nguyen, “High-Q VF μmechanical contour-mode disk resonators,” IEDM '00, pp. 399–402.    3. M. A. Abdelmoneum, M. U. Demirci, and C. T.-C. Nguyen, “Stemless wine-glass-mode disk μmech. resonators,” MEMS '03, pp. 698–701.    4. B. Bircumshaw, G. Liu, H. Takeuchi, T.-J. King, R. Howe, O. O'Reilly, A. Pisano, “The radial bulk annular resonator: towards a 50Ω RF MEMS filter, TRANSDUCERS '03, pp. 875–879.    5. G. Ambati, J. F. W. Bell, and J. C. K. Sharp, “In-plane vibrations of annular rings,” JOURNAL OF SOUND AND VIBRATION, Vol. 47, no. 3, pp. 415–432, 1976.    6. R. A. Johnson, “Mechanical Filters in Electronics,” New York, N.Y.; Wiley, 1983.    7. F. D. Bannon III, J. R. Clark, C. T.-C. Nguyen, “High-Q HF microelectromechanical Filters, IEEE J. SOLID-STATE CIRCUITS, Vol. 35, no. 4, pp. 512–526, April 2000
Having recently been demonstrated at frequencies past 1 GHz with Q's>1,500 in both vacuum and air [1], vibrating micromechanical (“μmechanical”) resonators are emerging as possible enablers for on-chip versions of the pre-select (or even channel-select) filters needed in the RF front-ends of wireless communication devices. The availability of such on-chip RF filters could greatly simplify the realization of future multi-band reconfigurable wireless communicators, which are expected to require many more RF filters than today's communicators—e.g., one set for each supported communication standard. Unfortunately, however, although their Q's and frequencies are now sufficient, the impedances of the GHz range μmechanical resonators demonstrated so far are still too high to allow direct coupling to antennas in RF systems, where matching to impedances in the range of 50Ω and 330Ω is often required.